This invention relates to bags. More specifically, this invention relates to an apparatus and process for manufacturing a dispensing unit of co-extruded thermoplastic T-shirt bags. In the dispensing unit of bags, a series of bags overlie one another and are interconnected for serial dispensing. When a first front bag is packed with groceries and removed from a rack containing the remainder of the dispensing unit of bags, an immediately subsequent second bag is automatically opened in preparation for loading in its own turn.